By Meghan Eisold

Recently, concussions have
been a major concern among soccer players. When I was in high-school, some
girls wore protective head gear, pictured below, to prevent concussions. I
decided to determine whether the headgear can significantly lower the force that
the ball exerts on a soccer player while heading the ball.

Mass of Soccer ball: 0.43 kg

Mass of soccer player’s: 75 kg

Horizontal Velocity of a kicked soccer ball(v

_{1}): 70 km/h (19.44 m/s)
I assumed that the Vertical Velocity of the ball is
negligible

Horizontal velocity of soccer player (v2): -5 km/h (-1.39 m/s)
(negative=direction soccer player is traveling)

Vertical Velocity of Soccer Player is assumed to be 0 (player is not
jumping)

First I determined the velocity of the ball and the
player after the collision:

**Elastic collisions**

Equation 1: m

_{1}v_{1 }+ m_{2}v_{2 }= m_{1}v_{1}^{’ }+m_{2}v_{2}^{’}
(0.43 kg)(19.44 m/s)+(75 kg)(-1.39 m/s)=(0.43
kg)v

_{1}^{’ }+(75 kg)v_{2}^{’}
Equation 2: v

_{1}+v_{1}^{’ }= v_{2}+ v_{2}^{’}
(19.44 m/s) +v

_{1}^{’ }= (0.43 kg) + v_{2}^{’}
v

_{1}^{’}= v_{2}^{’}– 19.01
Combine equations: (0.43 kg)(19.44 m/s)+(75
kg)(-1.39 m/s)=(0.43 kg)(v

_{2}^{’}– 19.01
m/s) +(75 kg)v

_{2}’
-95.89= -8.1743 +0.43v

_{2}^{’}+(75 kg)v_{2}’**v**_{2}^{’}=-1.16 m/s
(19.44 m/s) +v

_{1}^{’ }= (1.39 m/s) + (1.60 m/s)**v**_{1}^{’}=-19.21 m/s
I then used the final
velocities to determine the force that the ball would exert on the player
during the appropriate collision time. I estimated that the headgear would
extend the collision time by 5 ms.

Collision without headgear: t=25 ms =0.0025s

∑

*F*Δ*t*= Δ*p*
∑

*F*(0.0025s)=(75 kg)(-1.16 m/s)-( 75 kg)(-1.39 m/s)_{b on p}**∑**

*F*_{b on p}=**6900 N**

Collision with Collision
with headgear: t=30 ms =0.0030s

∑

*F*Δ*t*= Δ*p*
∑

*F*(0.0030s)=(75 kg)(-1.16 m/s)-( 75 kg)(-1.39 m/s)_{b on p}**∑**

*F*_{b on p}=**5750 N**

From
these results I can conclude that the headgear does lower the force that is
exerted on the player, but it is not a significant difference.

^{}
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